# Direction of Torque

1. Jun 19, 2015

### robbertypob

Hi

I've been learning about angular momentum and torque, and today I learned that torque actually has a direction that is not simply the direction of rotation.

I saw about the right-hand rule to establish which direction the torque is going in.

My question is - if an object is rotating, will it naturally want to travel in the direction of the torque generated? Is that how gyroscopes work?

Another question is what is the difference between torque and angular momentum? Does angular momentum generate torque?

Thanks!

2. Jun 19, 2015

### Orodruin

Staff Emeritus
No, this depends on the moment of inertia tensor. It is only true if the torque is directed along one of the eigenvectors of the moment of inertia.

The relation is the same as the relation between force and linear momentum, with the torque playing the role of the force and the angular momentum playing the role of the linear momentum. The role of the mass is played by the moment of inertia tensor.

3. Jun 19, 2015

### RyanH42

$τ=\vec{r}x\vec{F}$ and $τ=d\vec{L}/dt$ so time derivative of angular momentum is torque.

4. Jun 19, 2015

### robbertypob

Thank you. So if the object doesn't actually travel in the direction of the torque then when does the torque direction become relevant? Does the direction have any effect on anything?

On the second point - is the angular momentum actually generating torque on the axil? Would we say that? There must be torque present but how would we say it is generated?

5. Jun 19, 2015

### Orodruin

Staff Emeritus
The torque is always relevant. An unbalanced torque will lead to angular acceleration just as an unbalanced force will lead to acceleration.

Yes, it determines the direction of the angular acceleration (together with the moment of inertia tensor).

No, it is the other way around. An applied torque implies a change in the angular momentum. There is no need for a torque to be present in general, it just means the angular momentum is not changing.

6. Jun 19, 2015

### robbertypob

Imagining a bicycle wheel moving forward, from the perspective of the cyclist and using the right-hand rule, the direction of the torque would be to the left, correct? But the rider doesn't feel a sensation of being 'pulled' to the left by the torque. How can this be? Is there an opposing force balancing the wheel?

7. Jun 19, 2015

### Orodruin

Staff Emeritus
Unless the bicycle is accelerating, there is no net torque on the wheel as it maintains constant angular momentum. I believe you are mixing angular momentum and torque.

A torque is not a force. In fact, it is also not a vector but a pseudo vector, i.e., it does not change sign under reflections.

8. Jun 20, 2015

### tfr000

The "direction" is just the direction of the rotation axis. It is perpendicular to the rotation. Mathematically, it falls out of the definition of torque, the cross product of the force vector and the radius vector.

A torque acting over time = a change in angular momentum
the time rate of change of angular momentum = torque